FM 2004-3; versione 0.1 31/03/2004

**Authors**: Alessandro Giuliani,
Vieri Mastropietro

**Title**:
Anomalous universality in the
Anisotropic Ashkin--Teller model

**Abstract**:
The Ashkin--Teller (AT) model
is a generalization of Ising 2--d
to a four states spin model; it can be written in the form
of two Ising layers (in general
with different couplings)
interacting via a four--spin interaction.
It was conjectured long ago (by Kadanoff and Wegner,
Wu and Lin, Baxter and others) that
AT has in general two critical points, and that universality holds,
in the sense that the critical exponents are the same as in the Ising model,
except when the couplings of the two Ising layers are equal (isotropic case).
We obtain an explicit expression for the specific
heat from which we prove this conjecture in the
weakly interacting case
and we locate precisely the critical points.
We find the somewhat unexpected feature that,
despite universality holds for the specific heat,
nevertheless nonuniversal critical indexes
appear: for instance the distance between
the critical points rescales with an anomalous exponent
as we let the couplings of the two Ising layers
coincide (isotropic limit); and so does the
constant in front of the logarithm in the specific heat.
Our result also explains
how the crossover from universal to nonuniversal
behaviour is realized.

**Key words**: Anisotropic Ashkin-Teller model,
nonuniversal critical exponents,
renormalization group

Alessandro Giuliani

Fisica, Universita' di Roma "La Sapienza"

P.zzale Aldo Moro

Roma, Italia

em: alessandro.giuliani@roma1.infn.it

Vieri Mastropietro

Matematica, Universita' di Roma 2

Via della Ricerca Scientifica

Roma, Italia

em: mastropi@mat.uniroma2.it